Question 1

To study the effects of a new mathematics textbook, 30 students are randomly selected. Based on the scores of their achievement test, students are grouped into three groups (limited: 0-15, proficient: 16-30, advanced: 31-45). Half of the students in each group are then randomly assigned to use the new textbook, while the rest of the students continue to use the old textbook. Which of the following methods of blocking is employed here?

Accepted Answer

The method of blocking used here is predefined range blocking, as students are grouped into blocks based on predefined ranges of their achievement test scores before being randomly assigned to different treatments.

Question 2

In the scenario described above, instead of using the raw scores, the researcher used the percentile rank in the achievement test and grouped the students into three new groups: the top third, the middle third, and the bottom third. Then half of the students in each group were randomly assigned to use the new textbook. Which of the following methods of blocking is employed here?

Accepted Answer

Predefined value blocking is used when the researcher has a specific value or set of values that they want to use to create the blocks. In this case, the researcher used the percentile rank in the achievement test to create three blocks: the top third, the middle third, and the bottom third.

Question 3

Ravi was studying the effect of a new medicine on subjects' blood pressure. He randomly sampled 60 laboratory rats and ranked them based on their current blood pressure. Those ranked from 1 to 3 (i.e., the three rats with the highest blood pressure) formed group 1, and those ranked from 4 to 6 formed group 2, etc. Ravi then randomly selects five groups (i.e., 15 rats). Within each group, rats were randomly assigned to three groups: new medicine, old medicine, and no medicine. Which of the following methods of blocking is employed here?

Accepted Answer

Ravi used "sampled range blocking" by first ranking all subjects based on a specific criterion (blood pressure) and then forming groups based on these rankings before randomly assigning treatments within these groups.

Question 4

Azita wants to evaluate the effects of two new types of word processors (Macrosoft word and Toggle doc) on employees' working efficiency. Twelve employees were randomly selected and grouped into four blocks based on the nature of the work (proofreading, copyediting, technical writing, data analysis). Within each block, each employee was randomly assigned to use one of the three word processors: Macrosoft word, Toggle doc, and the old word processor. Their working efficiency as measured by the number of files processed per day was compared. Which of the following statements is false?

Accepted Answer

The answer of Azita wants to evaluate the effects of...

Question 5

In a split-plot design, suppose A is the between-subjects factor, B is the within- subjects factor, and S is the subject. Which of the following statements is true?

Accepted Answer

In a split-plot design, subjects are grouped according to the levels of the between-subjects factor (A), and then different levels of the within-subjects factor (B) are applied within these groups. This means that each subject is unique to a particular level of factor A, hence, subject (S) is nested within factor A.

Question 6

To study the effects of diet plans on blood pressure, the researcher assigned 10 subjects to diet plan A, and 10 participants to diet plan B. Within each group, five of the subjects are male and five participants are female. Which of the following statement is true?

Accepted Answer

Gender and diet plan are crossed because each level of one factor (gender) appears in combination with each level of the other factor (diet plan), allowing for the examination of the effects of diet plans on blood pressure across both genders.

Question 7

If a design is denoted by A(BC), it means that

Accepted Answer

The answer of If a design is denoted by A(BC),...

Question 8

If a design is denoted by A(BC), and there are four observations in each cell, which of the following effects can be studied?

Accepted Answer

In the design A(BC), A is the main factor and BC is a nested factor within A. Therefore, the interaction between B and C can be studied, but not interactions involving A with B or C.

Question 9

To determine if statistical software A is uniformly superior to software B for the population of statistical consultants, from which random samples are taken to conduct a study, one needs

Accepted Answer

The answer of To determine if statistical software A is...

Question 10

For the same course in statistics, two instructors are from the mathematics department, and two instructors are from the statistics department. Each instructor taught one session of the course (one student may only be enrolled in one session). The researcher is interested in comparing student evaluation of instructors from different departments. This is an example of which type of design?

Accepted Answer

This is a hierarchical design because the instructors are nested within their respective departments, and the researcher is interested in comparing the evaluations based on the department, not individual instructors.

Question 11

In the scenario as described in Question 10, suppose the instructors from the same department are randomly assigned to use either the lecture-based method or the computer-based method. The researcher is primarily interested in the effects of different instructional methods on student outcomes. Which of the following statements is correct?

Accepted Answer

The answer of In the scenario as described in Question...

Question 12

How many hypotheses are tested in a design denoted by A(B)?

Accepted Answer

In a design denoted by A(B), two hypotheses are typically tested: one for the main effect of A and one for the effect of B nested within A.

Question 13

In which of the following designs can we test the A × B interaction?

Accepted Answer

In a crossed design, both factors A and B are applied to all levels of each other, allowing for the testing of interactions between the two factors. Having n = 2 (or more) replicates per cell (combination of levels of A and B) provides enough data to estimate the variability necessary to test for interactions statistically.

Question 14

based on the following figure.
  Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected.
-Which of the following best describes the design of the experiment?

Accepted Answer

The notation A(B) typically indicates a nested design, where factor B is nested within factor A, suggesting that the levels of factor B are unique to each level of factor A.

Question 15

based on the following figure. Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected. -A is a random-effects factor and B is a fixed-effects factor. Each cell has 5 observations. The F_B ratio has degrees of freedom equal to?

Accepted Answer

The answer of based on the following figure.
  Each...

Question 16

based on the following figure. Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected. -Both A and B are fixed-effects factors. Each cell has 5 observations. The F_B ratio has degrees of freedom equal to?

Accepted Answer

2, 24The notation F_B refers to a two-way ANOVA without replication, where FS1 and BS1 represent the two factors (A and B) with their respective levels, and U1 represents the interaction between these factors. Given each cell has 5 observations and assuming there are no missing values, the degrees of freedom for the numerator (interaction between factors A and B) is calculated as (levels of A - 1) * (levels of B - 1) = 1 * 1 = 1. However, the notation suggests an additional factor or a mistake in the notation. Assuming a standard two-way ANOVA setup, the degrees of freedom for the denominator (error/residual) is calculated as total observations - [(levels of A) * (levels of B)] = 5*number of cells - number of cells = (number of cells - 1). Without the exact number of levels for A and B, we can't directly calculate the degrees of freedom for the error term. However, the correct interpretation for a typical two-way ANOVA with interaction and assuming "2, 24" as an option, suggests a misunderstanding in the question's notation. The correct calculation for a typical scenario with multiple observations per cell would involve the total number of observations minus the degrees of freedom for the main effects and interaction. Without specific details on the levels of A and B, "2, 24" could be interpreted as a placeholder for a scenario with a specific setup not detailed in the question, but this does not align with standard ANOVA calculations. The correct answer should reflect the degrees of freedom for the main effects and interaction based on the levels of A and B, and the total number of observations, which is not clearly provided in the question.

Question 17

based on the following figure. Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected. -Both A and B are random-effects factors. Each cell has 5 observations. The F_B ratio has degrees of freedom equal to?

Accepted Answer

The answer of based on the following figure.
  Each...

Question 18

If the correlation between the concomitant variable and dependent variable is −.35, and the concomitant variable is measured on an interval scale, which of the following designs is recommended?

Accepted Answer

The answer of If the correlation between the concomitant variable...

Question 19

If the correlation between the concomitant variable and dependent variable is .05, and the concomitant variable is measured on an ordinal scale, which of the following designs is recommended?

Accepted Answer

The answer of If the correlation between the concomitant variable...

Question 20

If the correlation between the concomitant variable and dependent variable is .5, and the concomitant variable is measured on an ordinal scale, which of the following designs is recommended?

Accepted Answer

Randomized block ANOVA is suitable when dealing with ordinal data and can help control for the concomitant variable's effect.

Quiz 16: Hierarchical and Randomized Block Analysis of Variance Models